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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Infinite conjugacy class property ： ウィキペディア英語版 Infinite conjugacy class property In mathematics, a group is said to have the infinite conjugacy class property, or to be an icc group, if the conjugacy class of every group element but the identity is infinite.〔.〕 The von Neumann group algebra of a group is a factor if and only if the group has the infinite conjugacy class property. It will then be, provided the group is nontrivial, of type ''II1'', i.e. it will possess a unique, faithful, tracial state.〔. See in particular p. 450: "''L''Γ is a II1 factor iff Γ is ICC".〕 Examples for icc groups are the group of permutations of finitely many elements of an infinite set,〔, p. 908.〕 and free groups on two generators.〔 In abelian groups, every conjugacy class consists of only one element, so icc groups are, in a way, as far from being abelian as possible. ==References== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Infinite conjugacy class property」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.